Slide 1

Report
2007 Pulsed Power and Plasma Science Conference
Albuquerque, NM
6E5  Dispersion relation of dust
acoustic waves in a DC glow
discharge plasma
Bob Merlino, Ross Fisher, Univ. Iowa
Ed Thomas, Jr. Auburn Univ.
Work supported by NSF and DOE
Dust acoustic waves
(Rao, Shukla, Yu, Planet. Space. Sci. 38, 543, 1990)
• very low frequency (<< wp+, phase speed
Csd << v+,th) longitudinal compressional
disturbances in a fluid-like dusty plasma
• the dust particles participate in the wave
dynamics – it is a “dust wave”
• phase speed (dust acoustic speed)
CDA
kT
~ Z
md
2
Dust acoustic waves: fluid theory
Dust
dynamics
Electrons
& Ions
Quasineutrality
K Dd  1
nd  (nd vd )

0
t
x
vd 
nd

 vd
md nd 
 vd
 kTd
 eZ d nd
0

x 
x
x
 t
ne
n


kTe
 ene
 0;
kT
 en
0
x
x
x
x
   (e  o )(n  ne  Znd )
2
n  ne  Z d nd
Combining the dust momentum equation with
the plasma equations we see that (for the case
of cold dust, Td = 0).
vd

md nd
  ( Pe  P )
t
x
where Pe + P+ is the total pressure due to
electrons and ions.
In the dust acoustic wave the inertia is
provided by the massive dust particles and the
electrons and ions provide the restoring force
excitation of dust acoustic waves
• dust acoustic waves can be driven by an
ion-dust streaming instability (Rosenberg,
JVST A 14, 631, 1996)
• a relatively modest drift uo~ vith of the ions
through the dust is sufficient for instability
• DAWs are spontaneously excited in dusty
plasmas produced in gas discharges
• are observed visually by laser light
scattering
dust acoustic dispersion relationship (Td ~ 0)
acoustic modes (long wavelength)






2

w  kT 
Z

 

K  md   T 
1   1  Z  



  Te 

n
w here:   d
ni
Finite KD effects:
w
K

w here:
2D

1
2De
2
w
 CDA
K
Effect of dust-gas collisions:
2
w w  ib   K 2CDA
1
2
 C DA  2

2 2 
1  K D 
1
1
b is the dust-neutral collision
frequency

1
2Di
Dust acoustic waves
cm
Measurement of the dispersion
relationship of the dust acoustic wave
Original Experiments
A. Barkan, N. D’Angelo, and R. L. Merlino, Phys. Plasmas, 2, 3563 (1995).
C. Thompson, A. Barkan, N. D’Angelo, and R. L. Merlino, Phys. Plasmas, 4, 2331 (1997).
New measurements of dust acoustic waves
• Over the past decade, numerous
experimental and theoretical studies of
DAW’s have been made.
• These studies have all been in the “linear”
regime of the DAW dispersion.
• Goal of new studies: extend dispersion
relation measurements to finite kD
regime.
UI dusty plasma device
Ar, 50 -150 mtorr
LASER
ANODE
GLOW
B
ANODE
DUST
300 – 400 V
~ 1 mA
Parameters
plasma density ~ 108 – 109 cm-3
Te ~ 2 – 3 eV, T+ ~ 0.025 eV
Dust: kaolin powder -average dust radius ~ 1 micron
average dust charge Z ~ – (1000 – 2000)
dust density nd ~ 105 cm-3, wpd ~ 300 - 500 s-1
For current
modulation
60 cm dia. x 80 cm long vacuum vessel
dc glow discharge plasmas (N2, Ar)
50 - 100 G axial magnetic fields
Experiment at Univ.
of Iowa, Fall, 2006
Dust acoustic waves are captured using
a 30 fps digital camera
single frame video images of DAW
Natural
65 kHz
39 kHz
130 kHz
video analysis
About 100 images were analyzed for each frequency
w (s–1)
dispersion relation
(long wavelength)
K (cm–1)
dispersion relation  short wavelengths
Td = 40 eV
w (s
) )
w
(s–1–1
Td = 10 eV
K (cm–1)
Hot dust?
• J. Williams and E. Thomas, Jr. (IEEE TPS
35, 303, 2007) measured dust
temperatures for dust embedded in a dc
glow discharge
• Method- stereoscopic particle image
velocimetry, determined Td in 3 directions
• Found Td’s ~ tens of eV at comparable
pressures as those used here
Weakly vs. strongly coupled?
1000
2
d
Q

4 o  kTd
100

10
1
0.1
0.01
0.1
1
10
Dust temperature, eV
If dust were cold,  would be large and dust
would be in strongly coupled state, which it isn’t.
100
summary
• DAWs were investigated in a dc glow discharge
plasma
• DAWs appear spontaneously, but their
frequency can be controlled by modulating the
discharge current
• Frequencies up to ~ 200 Hz were studied to
measure the DAW dispersion relation
• interference of spontaneously excited DAW and
high frequency, imposed DAW was observed
• Comparison with theory requires that the dust is
hot, with Td ~ 10s of eV.

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